Multi-Time Unscented Kalman Inversion for Calibration of Expensive Chaotic Models

Abstract

Computer models traditionally used for weather and climate prediction have extremely high computational costs, which impedes their use in infrastructure design decisions, scientific exploration, and uncertainty quantification. While reduced models exist, they have limited utility because they are unable to reliably emulate the behavior of the relevant detailed models. In part, this is because their calibration poses a host of difficulties, including chaotic dynamics that prevent the use of adjoint methods, computational costs that become unreasonable when sampling approaches require many forward runs, and large existing code bases that require black box approaches. Recently, methods based on Kalman ensembles have shown promise by providing approximate derivatives of parameters in black box models in order to reach convergence using relatively few forward model runs. Another set of strategies for reducing computation costs are multi-fidelity methods, which combine various resolution model runs. Building on these approaches, and inspired by work in consistency testing for climate models, we propose an approach that utilizes ultra-short model runs to help improve calibration performance for reduced models, while still using full length runs to ensure convergence for the relevant quantities of interest. In contrast to other multi-fidelity methods we are able to use the same model resolution throughout calibration, addressing the issue that parameter selections in climate models are often resolution dependent. We show a strong reduction in computation cost on both classical chaotic test cases and reduced sub-grid models as part of a full global circulation model.